Pre-Algebra Examples

$\frac{{(x - 8)}^{2}}{x^{2} - 64}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $64$ as $8^{2}$ .

$\frac{{(x - 8)}^{2}}{x^{2} - 8^{2}}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 8$ .

$\frac{{(x - 8)}^{2}}{(x + 8) (x - 8)}$

Step 2

Cancel the common factor of ${(x - 8)}^{2}$ and $x - 8$ .

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Step 2.1

Factor $x - 8$ out of ${(x - 8)}^{2}$ .

$\frac{(x - 8) (x - 8)}{(x + 8) (x - 8)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x - 8$ out of $(x + 8) (x - 8)$ .

$\frac{(x - 8) (x - 8)}{(x - 8) (x + 8)}$

Step 2.2.2

Cancel the common factor.

$\frac{(x - 8) (x - 8)}{(x - 8) (x + 8)}$

Step 2.2.3

Rewrite the expression.

$\frac{x - 8}{x + 8}$